Open Access
Translator Disclaimer
2010 Stochastic Domination for the Ising and Fuzzy Potts Models
Marcus Warfheimer
Author Affiliations +
Electron. J. Probab. 15: 1802-1824 (2010). DOI: 10.1214/EJP.v15-820

Abstract

We discuss various aspects concerning stochastic domination for the Ising model and the fuzzy Potts model. We begin by considering the Ising model on the homogeneous tree of degree $d$, $\mathbb{T}^d$. For given interaction parameters $J_1$, $J_2>0$ and external field $h_1\in\mathbb{R}$, we compute the smallest external field $\tilde{h}$ such that the plus measure with parameters $J_2$ and $h$ dominates the plus measure with parameters $J_1$ and $h_1$ for all $h\geq\tilde{h}$. Moreover, we discuss continuity of $\tilde{h}$ with respect to the three parameters $J_1$, $J_2$, $h_1$ and also how the plus measures are stochastically ordered in the interaction parameter for a fixed external field. Next, we consider the fuzzy Potts model and prove that on $\mathbb{Z}^d$ the fuzzy Potts measures dominate the same set of product measures while on $\mathbb{T}^d$, for certain parameter values, the free and minus fuzzy Potts measures dominate different product measures

Citation

Download Citation

Marcus Warfheimer. "Stochastic Domination for the Ising and Fuzzy Potts Models." Electron. J. Probab. 15 1802 - 1824, 2010. https://doi.org/10.1214/EJP.v15-820

Information

Accepted: 14 November 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1227.60110
MathSciNet: MR2738339
Digital Object Identifier: 10.1214/EJP.v15-820

Subjects:
Primary: 60K35

Keywords: domination of product measures , fuzzy Potts model , Ising model , stochastic domination

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.15 • 2010
Back to Top